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arXiv:2308.10063

Tomonaga-Luttinger liquid-Bose glass phase transition in a system of 1D disordered fermions with pair hoppings

M. S. Bahovadinov, R. O. Sharipov, B. L. Altshuler, Gora V. Shlyapnikov

Published Aug 19, 2023• 0 citations
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Abstract

We consider a one-dimensional system of spinless fermions with single particle and pair hoppings in a potential on-site disorder. The pair hopping term violates integrability of the model and enhances superconducting fluctuations in the bulk of the liquid. By means of the Abelian bosonization and extensive numerical DMRG calculations we provide evidence that sufficiently large pair hopping amplitude guarantees the survival of the Tomonaga-Luttinger liquid phase at weak disorder. Large disorder drives the system to the Bose glass phase, realising the Giamarchi-Schulz scenario in such a system.

DOI
10.48550/arxiv.2308.10063

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We consider a one-dimensional system of spinless fermions with single particle and pair hoppings in a potential on-site disorder. The pair hopping term violates integrability of the model and enhances superconducting fluctuations in the bulk of the liquid. By means of the Abelian bosonization and extensive numerical DMRG calculations we provide evidence that sufficiently large pair hopping amplitude guarantees the survival of the Tomonaga-Luttinger liquid phase at weak disorder. Large disorder drives the system to the Bose glass phase, realising the Giamarchi-Schulz scenario in such a system.
We consider a one-dimensional system of spinless fermions with single particle and pair hoppings in a potential on-site disorder. The pair hopping term violates integrability of the model and enhances superconducting fluctuations in the bulk of the liquid. By means of the Abelian bosonization and extensive numerical density matrix renormalization group calculations we provide evidence that sufficiently large pair hopping amplitude guarantees the survival of the Tomonaga-Luttinger liquid phase at weak disorder. Large disorder drives the system to the Bose-glass phase, realizing the Giamarchi-Schulz scenario in such a system.
We study the superfluid--Bose-glass transition in a one-dimensional lattice boson model with power-law decaying hopping amplitude ${t}_{i\ensuremath{-}j}\ensuremath{\sim}1/{|i\ensuremath{-}j|}^{\ensuremath{\alpha}}$, using bosonization and the nonperturbative functional renormalization group (FRG). When $\ensuremath{\alpha}$ is smaller than a critical value ${\ensuremath{\alpha}}_{c}<3$, the U(1) symmetry is spontaneously broken, which leads to a density mode with nonlinear dispersion and dynamical exponent $z=(\ensuremath{\alpha}\ensuremath{-}1)/2$; the superfluid phase is then stable for sufficiently weak disorder, contrary to the case of short-range hopping where disorder is a relevant perturbation when the Luttinger parameter is smaller than 3/23/23/2. In the presence of disorder, however, long-range hopping has no effect in the infrared limit and the FRG flow eventually becomes similar to that of a boson system with short-range hopping. This implies that the superfluid phase, when stable, exhibits a density mode with linear dispersion (z=1z=1z=1) and the superfluid--Bose-glass transition remains in the Berezinskii-Kosterlitz-Thouless universality class, while the Bose-glass fixed point is insensitive to long-range hopping. We compare our findings with a recent numerical study.
Interacting one-dimensional bosons with long range hopping decaying as a power law r−αr^{-α}r−α with distance rrr are considered with the renormalization group and the self-consistent harmonic approximation. For α≥3α\ge 3α≥3, the ground state is always a Tomonaga-Luttinger liquid, whereas for α<3α<3α<3, a ground state with long range order breaking the continuous global gauge symmetry becomes possible for sufficiently weak repulsion. At positive temperature, continuous symmetry breaking becomes restricted to α<2α<2α<2, and for 2<α<32<α<32<α<3, a Tomonaga-Luttinger liquid with the Tomonaga-Luttinger exponent diverging at low temperature is found.
We revisit the low-energy physics of one-dimensional spinless fermion liquids, showing that with sufficiently strong interactions the conventional Luttinger liquid can give way to a strong-pairing phase. While the density fluctuations in both phases are described by a gapless Luttinger liquid, single fermion excitations are gapped only in the strong-pairing phase. Smooth spatial Interfaces between the two phases lead to topological degeneracies in the ground-state and low-energy spectrum of the density fluctuations. Using a concrete microscopic model, with both single-particle and pair hopping, we show that the strong-pairing state is established through emergence of a new low-energy fermionic mode. We characterize the two phases with numerical calculations using the density matrix renormalization group. In particular we find enhancement of the central charge from c=1c=1c=1 in the two Luttinger liquid phases to c=3/2c=3/2c=3/2 at the critical point, which gives direct evidence for an emergent critical Majorana mode. Finally, we confirm the existence of topological degeneracies in the low-energy phonon spectrum, associated with spatial interfaces between the two phases.
The low-temperature phase diagram of one-dimensional weakly disordered quantum systems such as charge or spin density waves and Luttinger liquids is studied by a full finite temperature renormalization-group (RG) calculation. For vanishing quantum fluctuations this approach is amended by an exact solution in the case of strong disorder and by a mapping onto the Burgers equation with noise in the case of weak disorder, respectively. At zero temperature we reproduce the quantum phase transition between a pinned (localized) and an unpinned (delocalized) phase for weak and strong quantum fluctuations, respectively, as found previously by Fukuyama or Giamarchi and Schulz. At finite temperatures the localization transition is suppressed: the random potential is wiped out by thermal fluctuations on length scales larger than the thermal de Broglie wavelength of the phason excitations. The existence of a zero-temperature transition is reflected in a rich crossover phase diagram of the correlation functions. In particular we find four different scaling regions: a classical disordered, a quantum disordered, a quantum critical, and a thermal region. The results can be transferred directly to the discussion of the influence of disorder in superfluids. Finally we extend the RG calculation to the treatment of a commensurate lattice potential. Applications to related systems are discussed as well.